From samples of pp collision data collected by the LHCb experiment at root s = 7, 8 and 13 TeV, corresponding to integrated luminosities of 1.0, 2.0 and 1.5 fb(-1), respectively, a peak in both the Lambda(0)(b) K- and Xi(0)(b)pi(-) invariant mass spectra is observed. In the quark model, radially and orbitally excited Xi(-)(b) resonances with quark content bds are expected. Referring to this peak as Xi(b)(6227)(-), the mass and natural width are measured to be m(Xi b(6227))(-) = 6226.9 +/- 2.0 +/- 0.3 +/- 0.2 MeV/c(2) and Gamma(Xi b(6227))- = 18.1 +/- 5.4 +/- 1.8 MeV/c(2), where the first uncertainty is statistical, the second is systematic, and the third, on m(Xi b(6227))(-), is due to the knowledge of the Lambda(0)(b) baryon mass. Relative production rates of the Xi(b)(6227)(-) -> Lambda K-0(b)- and Xi(b)(6227)(-) -> Xi(0)(b)pi(-) decays are also reported.